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 Documentation Ver 1.0.0 August 2011 by
 <a href="http://mmc.geofisica.unam.mx/luiggi">Luis M. de la Cruz</a> <br>
 <a href="http://mmc.geofisica.unam.mx"> GMMC </a> -
 <a href="http://www.geofisica.unam.mx/recnat/"> Depto. de Recursos Naturales </a> -
 <a href="http://www.geofisica.unam.mx"> Instituto de Geof&iacute;sica </a> -
 <a href="http://www.unam.mx"> UNAM </a><br>
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<div class="title">Examples/05ConvDiffForced/convection1.cpp</div>  </div>
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<a href="convection1_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 
<a name="l00034"></a>00034 <span class="preprocessor">#include &lt;iostream&gt;</span>
<a name="l00035"></a>00035 <span class="preprocessor">#include &lt;cmath&gt;</span>
<a name="l00036"></a>00036 <span class="preprocessor">#include &quot;Meshes/Uniform.hpp&quot;</span>
<a name="l00037"></a>00037 <span class="preprocessor">#include &quot;Equations/ScalarEquation.hpp&quot;</span>
<a name="l00038"></a>00038 
<a name="l00039"></a>00039 <span class="preprocessor">#ifdef WITH_CDS_CoDi</span>
<a name="l00040"></a>00040 <span class="preprocessor"></span><span class="preprocessor">#include &quot;Schemes/CDS_CoDi.hpp&quot;</span>
<a name="l00041"></a>00041 <span class="preprocessor">#endif</span>
<a name="l00042"></a>00042 <span class="preprocessor"></span>
<a name="l00043"></a>00043 <span class="preprocessor">#ifdef WITH_CDS_Hay</span>
<a name="l00044"></a>00044 <span class="preprocessor"></span><span class="preprocessor">#include &quot;Schemes/CDS_Hay.hpp&quot;</span>
<a name="l00045"></a>00045 <span class="preprocessor">#endif</span>
<a name="l00046"></a>00046 <span class="preprocessor"></span>
<a name="l00047"></a>00047 <span class="preprocessor">#ifdef WITH_Upwind_CoDi</span>
<a name="l00048"></a>00048 <span class="preprocessor"></span><span class="preprocessor">#include &quot;Schemes/Upwind_CoDi.hpp&quot;</span>
<a name="l00049"></a>00049 <span class="preprocessor">#endif</span>
<a name="l00050"></a>00050 <span class="preprocessor"></span>
<a name="l00051"></a>00051 <span class="preprocessor">#ifdef WITH_Quick_CoDi</span>
<a name="l00052"></a>00052 <span class="preprocessor"></span><span class="preprocessor">#include &quot;Schemes/Quick_CoDi.hpp&quot;</span>
<a name="l00053"></a>00053 <span class="preprocessor">#endif</span>
<a name="l00054"></a>00054 <span class="preprocessor"></span>
<a name="l00055"></a>00055 <span class="preprocessor">#ifdef WITH_Quick_Hay</span>
<a name="l00056"></a>00056 <span class="preprocessor"></span><span class="preprocessor">#include &quot;Schemes/Quick_Hay.hpp&quot;</span>
<a name="l00057"></a>00057 <span class="preprocessor">#endif</span>
<a name="l00058"></a>00058 <span class="preprocessor"></span>
<a name="l00059"></a>00059 <span class="preprocessor">#include &quot;Solvers/TDMA.hpp&quot;</span>
<a name="l00060"></a>00060 <span class="preprocessor">#include &quot;Utils/inout.hpp&quot;</span> 
<a name="l00061"></a>00061 <span class="preprocessor">#include &quot;Utils/num_utils.hpp&quot;</span>
<a name="l00062"></a>00062 <span class="preprocessor">#include &quot;Utils/GNUplot.hpp&quot;</span>
<a name="l00063"></a>00063 <span class="keyword">using namespace </span>Tuna;
<a name="l00064"></a>00064   
<a name="l00065"></a>00065 <span class="comment">// Scalar field in one dimension</span>
<a name="l00066"></a>00066 <span class="keyword">typedef</span> <a class="code" href="structTuna_1_1TunaArray.html#af3bcab5018eec3d7697c9fb03ad89157" title="Definition of big arrays to store scalar fields on meshes.">TunaArray&lt;double,1&gt;::huge</a> ScalarField1D;
<a name="l00067"></a>00067 
<a name="l00068"></a>00068 <span class="keywordtype">void</span> exactSolution(ScalarField1D &amp;, <span class="keywordtype">double</span>, <span class="keywordtype">double</span>, <span class="keywordtype">double</span>, <span class="keywordtype">double</span>);
<a name="l00069"></a>00069 
<a name="l00070"></a>00070 <span class="keywordtype">int</span> pausa;
<a name="l00071"></a>00071 
<a name="l00072"></a>00072 <span class="keywordtype">int</span> main() 
<a name="l00073"></a>00073 {
<a name="l00074"></a>00074 
<a name="l00075"></a>00075 <span class="preprocessor">#ifdef WITH_GNUPLOT</span>
<a name="l00076"></a>00076 <span class="preprocessor"></span>    GNUplot plotter;
<a name="l00077"></a>00077     <span class="keywordtype">int</span> stop;
<a name="l00078"></a>00078     plotter(<span class="stringliteral">&quot;set grid&quot;</span>);
<a name="l00079"></a>00079 <span class="preprocessor">#endif</span>
<a name="l00080"></a>00080 <span class="preprocessor"></span>
<a name="l00081"></a>00081     <span class="keywordtype">double</span> length_x;
<a name="l00082"></a>00082     <span class="keywordtype">int</span> num_nodes_x;
<a name="l00083"></a>00083     <span class="keywordtype">double</span> right_wall = 0.0, left_wall = 1.0;
<a name="l00084"></a>00084     <span class="keywordtype">double</span> dt, error = 1.0, residual, G;
<a name="l00085"></a>00085     <span class="keywordtype">int</span> nmax, frequency, iteration = 1;
<a name="l00086"></a>00086 
<a name="l00087"></a>00087 <span class="comment">// Reading data from the input file</span>
<a name="l00088"></a>00088     std::ifstream input_cin (<span class="stringliteral">&quot;input1&quot;</span>); 
<a name="l00089"></a>00089     input_cin &gt;&gt; length_x
<a name="l00090"></a>00090               &gt;&gt; num_nodes_x 
<a name="l00091"></a>00091               &gt;&gt; G
<a name="l00092"></a>00092               &gt;&gt; dt
<a name="l00093"></a>00093               &gt;&gt; nmax
<a name="l00094"></a>00094               &gt;&gt; frequency;
<a name="l00095"></a>00095     input_cin.close();
<a name="l00096"></a>00096 
<a name="l00097"></a>00097     <a class="code" href="classTuna_1_1StructuredMesh.html" title="General structured meshes on rectangular domains.">StructuredMesh&lt;Uniform&lt;double, 1&gt;</a> &gt; mesh(length_x, num_nodes_x);
<a name="l00098"></a>00098     <span class="keywordtype">double</span> dx = mesh.getDelta(X);
<a name="l00099"></a>00099     <span class="keywordtype">int</span> num_vols_x = mesh.getExtentVolumes(X);
<a name="l00100"></a>00100     mesh.print();
<a name="l00101"></a>00101 
<a name="l00102"></a>00102     ScalarField1D T(mesh.getExtentVolumes());
<a name="l00103"></a>00103     ScalarField1D u(mesh.getExtentVolumes());
<a name="l00104"></a>00104     ScalarField1D us(num_nodes_x);         <span class="comment">// staggered u-velocity </span>
<a name="l00105"></a>00105 
<a name="l00106"></a>00106     ScalarField1D Tn(mesh.getExtentNodes());
<a name="l00107"></a>00107     ScalarField1D Ta(mesh.getExtentNodes());
<a name="l00108"></a>00108     ScalarField1D un(mesh.getExtentNodes());
<a name="l00109"></a>00109 
<a name="l00110"></a>00110     T = 0;
<a name="l00111"></a>00111     T(T.lbound(firstDim)) = left_wall;   
<a name="l00112"></a>00112     T(T.ubound(firstDim)) = right_wall;
<a name="l00113"></a>00113 
<a name="l00114"></a>00114     NumUtils::interpolateToNodes(Tn, T);
<a name="l00115"></a>00115     InOut::writeToFile(Tn, iteration, <span class="stringliteral">&quot;./Data1/temp.&quot;</span>, dx);
<a name="l00116"></a>00116 
<a name="l00117"></a>00117     un = 1;
<a name="l00118"></a>00118     NumUtils::staggerFromNodesX(us, un);
<a name="l00119"></a>00119 
<a name="l00120"></a>00120     SparseMatrix&lt; Diagonal&lt;double, 1 &gt; &gt; A(num_nodes_x);
<a name="l00121"></a>00121 
<a name="l00122"></a>00122     ScalarField1D              b(num_nodes_x);
<a name="l00123"></a>00123         
<a name="l00124"></a>00124 <span class="preprocessor">#ifdef WITH_CDS_CoDi</span>
<a name="l00125"></a>00125 <span class="preprocessor"></span>    <a class="code" href="classTuna_1_1ScalarEquation.html" title="This class derives from GeneralEquation through B &amp; N trick.">ScalarEquation&lt;CDS_CoDi&lt;double,1&gt;</a> &gt; conv_diff(T, A, b, mesh.getDeltas()); 
<a name="l00126"></a>00126 <span class="preprocessor">#endif</span>
<a name="l00127"></a>00127 <span class="preprocessor"></span>
<a name="l00128"></a>00128 <span class="preprocessor">#ifdef WITH_CDS_Hay</span>
<a name="l00129"></a>00129 <span class="preprocessor"></span>    <a class="code" href="classTuna_1_1ScalarEquation.html" title="This class derives from GeneralEquation through B &amp; N trick.">ScalarEquation&lt;CDS_Hay&lt;double,1&gt;</a> &gt; conv_diff(T, A, b, mesh.getDeltas()); 
<a name="l00130"></a>00130 <span class="preprocessor">#endif</span>
<a name="l00131"></a>00131 <span class="preprocessor"></span>
<a name="l00132"></a>00132 <span class="preprocessor">#ifdef WITH_Upwind_CoDi</span>
<a name="l00133"></a>00133 <span class="preprocessor"></span>    <a class="code" href="classTuna_1_1ScalarEquation.html" title="This class derives from GeneralEquation through B &amp; N trick.">ScalarEquation&lt;Upwind_CoDi&lt;double,1&gt;</a> &gt; conv_diff(T, A, b, mesh.getDeltas());
<a name="l00134"></a>00134 <span class="preprocessor">#endif</span>
<a name="l00135"></a>00135 <span class="preprocessor"></span>
<a name="l00136"></a>00136 <span class="preprocessor">#ifdef WITH_Quick_CoDi</span>
<a name="l00137"></a>00137 <span class="preprocessor"></span>    <a class="code" href="classTuna_1_1ScalarEquation.html" title="This class derives from GeneralEquation through B &amp; N trick.">ScalarEquation&lt;Quick_CoDi&lt;double,1&gt;</a> &gt; conv_diff(T, A, b, mesh.getDeltas());    
<a name="l00138"></a>00138 <span class="preprocessor">#endif</span>
<a name="l00139"></a>00139 <span class="preprocessor"></span>
<a name="l00140"></a>00140 <span class="preprocessor">#ifdef WITH_Quick_Hay</span>
<a name="l00141"></a>00141 <span class="preprocessor"></span>    <a class="code" href="classTuna_1_1ScalarEquation.html" title="This class derives from GeneralEquation through B &amp; N trick.">ScalarEquation&lt;Quick_Hay&lt;double,1&gt;</a> &gt; conv_diff(T, A, b, mesh.getDeltas());    
<a name="l00142"></a>00142 <span class="preprocessor">#endif</span>
<a name="l00143"></a>00143 <span class="preprocessor"></span>
<a name="l00144"></a>00144     conv_diff.setGamma(G);
<a name="l00145"></a>00145     conv_diff.setDeltaTime(dt);
<a name="l00146"></a>00146     conv_diff.setDirichlet(LEFT_WALL);
<a name="l00147"></a>00147     conv_diff.setDirichlet(RIGHT_WALL);
<a name="l00148"></a>00148     conv_diff.setUvelocity(us);
<a name="l00149"></a>00149     conv_diff.print();
<a name="l00150"></a>00150 
<a name="l00151"></a>00151     ofstream error_fp(<span class="stringliteral">&quot;./Data1/error&quot;</span>), residual_fp(<span class="stringliteral">&quot;./Data1/residual&quot;</span>);
<a name="l00152"></a>00152     <span class="keywordtype">int</span> Nerror;
<a name="l00153"></a>00153     <span class="keywordtype">double</span> errorL1, errorL2, errorLmax, errorL2_I, errorMS, errorMS_I;
<a name="l00154"></a>00154     <span class="keywordtype">double</span> AeL1, AeL2, AeLmax, ReL1, ReL2, ReLmax;
<a name="l00155"></a>00155     <span class="keywordtype">double</span> normL1, normL2, normLmax;
<a name="l00156"></a>00156     <a class="code" href="structTuna_1_1timer.html" title="Struct useful to measure the elapsed time.">timer</a> time;
<a name="l00157"></a>00157     <span class="keywordtype">double</span> total_time = 0.0;
<a name="l00158"></a>00158 
<a name="l00159"></a>00159     <span class="keywordflow">while</span> ( iteration &lt;= nmax ) {
<a name="l00160"></a>00160         time.<a class="code" href="structTuna_1_1timer.html#a5b0cf85d5db9b941e13ce7c79d7de7b0" title="Start the clock.">tic</a>();
<a name="l00161"></a>00161         conv_diff.calcCoefficients();
<a name="l00162"></a>00162         Solver::TDMA1D(conv_diff);
<a name="l00163"></a>00163         residual = conv_diff.calcResidual();
<a name="l00164"></a>00164         conv_diff.update();
<a name="l00165"></a>00165         total_time += time.<a class="code" href="structTuna_1_1timer.html#a3796592dd5b589521e1093d9225eee5e" title="Stop the clock and returns the elapsed time.">toc</a>();
<a name="l00166"></a>00166 
<a name="l00167"></a>00167         <span class="keywordflow">if</span> (!(iteration % frequency)) {
<a name="l00168"></a>00168           exactSolution(Ta, 1, iteration * dt , G, dx);
<a name="l00169"></a>00169           NumUtils::interpolateToNodes(Tn, T);
<a name="l00170"></a>00170           errorL1   = NumUtils::calcErrorL1(Tn, Ta);
<a name="l00171"></a>00171           errorL2   = NumUtils::calcErrorL2(Tn, Ta);
<a name="l00172"></a>00172           errorLmax = NumUtils::calcErrorLmax(Tn, Ta);
<a name="l00173"></a>00173           AeL1      = NumUtils::calcAbsoluteError_L1(Tn, Ta);
<a name="l00174"></a>00174           AeL2      = NumUtils::calcAbsoluteError_L2(Tn, Ta);
<a name="l00175"></a>00175           AeLmax    = NumUtils::calcAbsoluteError_Lmax(Tn, Ta);
<a name="l00176"></a>00176           normL1    = NumUtils::normL1(Ta);
<a name="l00177"></a>00177           normL2    = NumUtils::normL2(Ta);
<a name="l00178"></a>00178           normLmax  = NumUtils::normLmax(Ta);
<a name="l00179"></a>00179           ReL1      = AeL1 / normL1;
<a name="l00180"></a>00180           ReL2      = AeL2 / normL2;
<a name="l00181"></a>00181           ReLmax    = AeLmax / normLmax;
<a name="l00182"></a>00182           errorMS   = errorL2 * errorL2;
<a name="l00183"></a>00183           
<a name="l00184"></a>00184           <span class="comment">/* */</span>
<a name="l00185"></a>00185           errorL2_I = 0.0; Nerror = 0;  
<a name="l00186"></a>00186           <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i = Tn.lbound(firstDim)+1; i &lt;= Tn.ubound(firstDim)-1; ++i, ++Nerror) {
<a name="l00187"></a>00187             errorL2_I += (Tn(i) - Ta(i)) * (Tn(i) - Ta(i));
<a name="l00188"></a>00188           }
<a name="l00189"></a>00189           errorL2_I = sqrt(errorL2_I / Nerror);
<a name="l00190"></a>00190           errorMS_I = errorL2_I * errorL2_I;
<a name="l00191"></a>00191           <span class="comment">/* */</span>
<a name="l00192"></a>00192           <span class="comment">//    error_fp &lt;&lt; dt * iteration &lt;&lt; &quot;\t&quot; &lt;&lt; error &lt;&lt; std::endl;</span>
<a name="l00193"></a>00193           
<a name="l00194"></a>00194           cout &lt;&lt; <span class="stringliteral">&quot;\n ---- Iteration = &quot;</span> &lt;&lt; iteration
<a name="l00195"></a>00195                &lt;&lt; <span class="stringliteral">&quot;\n\n Residual = &quot;</span> &lt;&lt; residual &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>
<a name="l00196"></a>00196                &lt;&lt; <span class="stringliteral">&quot; Error L1 = &quot;</span> &lt;&lt; errorL1 &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span> 
<a name="l00197"></a>00197                &lt;&lt; <span class="stringliteral">&quot; Error L2 = &quot;</span> &lt;&lt; errorL2 &lt;&lt; <span class="stringliteral">&quot; I = &quot;</span> &lt;&lt; errorL2_I &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span> 
<a name="l00198"></a>00198                &lt;&lt; <span class="stringliteral">&quot; Error Lmax = &quot;</span> &lt;&lt; errorLmax &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span> 
<a name="l00199"></a>00199                &lt;&lt; <span class="stringliteral">&quot; Error MS = &quot;</span> &lt;&lt; errorMS &lt;&lt; <span class="stringliteral">&quot; I = &quot;</span> &lt;&lt; errorMS_I &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>
<a name="l00200"></a>00200                &lt;&lt; <span class="stringliteral">&quot; Error Absolute L1 = &quot;</span> &lt;&lt; AeL1 &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span> 
<a name="l00201"></a>00201                &lt;&lt; <span class="stringliteral">&quot; Error Absolute L2 = &quot;</span> &lt;&lt; AeL2 &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span> 
<a name="l00202"></a>00202                &lt;&lt; <span class="stringliteral">&quot; Error Absolute Lmax = &quot;</span> &lt;&lt; AeLmax &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span> 
<a name="l00203"></a>00203                &lt;&lt; <span class="stringliteral">&quot; Error Relative L1 = &quot;</span> &lt;&lt; ReL1 &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span> 
<a name="l00204"></a>00204                &lt;&lt; <span class="stringliteral">&quot; Error Relative L2 = &quot;</span> &lt;&lt; ReL2 &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span> 
<a name="l00205"></a>00205                &lt;&lt; <span class="stringliteral">&quot; Error Relative Lmax = &quot;</span> &lt;&lt; ReLmax &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>
<a name="l00206"></a>00206                &lt;&lt; <span class="stringliteral">&quot; Total time = &quot;</span> &lt;&lt; total_time &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;
<a name="l00207"></a>00207           
<a name="l00208"></a>00208           cout &lt;&lt; errorL1 &lt;&lt; <span class="stringliteral">&quot; &quot;</span> 
<a name="l00209"></a>00209                &lt;&lt; errorL2 &lt;&lt; <span class="stringliteral">&quot; &quot;</span> 
<a name="l00210"></a>00210                &lt;&lt; ReL1 &lt;&lt; <span class="stringliteral">&quot; &quot;</span>
<a name="l00211"></a>00211                &lt;&lt; ReL2 &lt;&lt; <span class="stringliteral">&quot; &quot;</span>
<a name="l00212"></a>00212                &lt;&lt; ReLmax &lt;&lt; <span class="stringliteral">&quot; &quot;</span>
<a name="l00213"></a>00213                &lt;&lt; ReLmax &lt;&lt; <span class="stringliteral">&quot; &quot;</span>
<a name="l00214"></a>00214                &lt;&lt; residual &lt;&lt; <span class="stringliteral">&quot; &quot;</span>
<a name="l00215"></a>00215                &lt;&lt; total_time &lt;&lt; <span class="stringliteral">&quot;\n\n&quot;</span>;
<a name="l00216"></a>00216 
<a name="l00217"></a>00217           InOut::writeToFile(Ta, 1, <span class="stringliteral">&quot;./Data1/exac.&quot;</span>, dx);
<a name="l00218"></a>00218           InOut::writeToFile(Tn, 1, <span class="stringliteral">&quot;./Data1/temp.&quot;</span>, dx);
<a name="l00219"></a>00219           
<a name="l00220"></a>00220           <span class="comment">/* */</span>
<a name="l00221"></a>00221 <span class="preprocessor">#ifdef WITH_GNUPLOT</span>
<a name="l00222"></a>00222 <span class="preprocessor"></span>          std::cout &lt;&lt; <span class="stringliteral">&quot;\n &gt;---&gt; Press &lt;1&gt; and then &lt;enter&gt; to continue \n&quot;</span>;
<a name="l00223"></a>00223           std::cin &gt;&gt; stop;     
<a name="l00224"></a>00224           plotter(<span class="stringliteral">&quot;p [0:2.5][-0.25:1.5] \&quot;Data1/temp.00001\&quot; w l title \&quot;Numerical Simulation\&quot;, \&quot;Data1/exac.00001\&quot; title \&quot;Exact solution\&quot; w l &quot;</span>);
<a name="l00225"></a>00225 <span class="preprocessor">#endif</span>
<a name="l00226"></a>00226 <span class="preprocessor"></span>          <span class="comment">/* */</span>
<a name="l00227"></a>00227         }           
<a name="l00228"></a>00228 
<a name="l00229"></a>00229         cout &lt;&lt; <span class="stringliteral">&quot;\n ---- Iteration = &quot;</span> &lt;&lt; iteration;
<a name="l00230"></a>00230         ++iteration;
<a name="l00231"></a>00231     }
<a name="l00232"></a>00232 
<a name="l00233"></a>00233     <span class="keywordflow">return</span> 0;
<a name="l00234"></a>00234 }
<a name="l00235"></a>00235 
<a name="l00236"></a>00236 <span class="keywordtype">void</span> exactSolution(ScalarField1D &amp;Ta, <span class="keywordtype">double</span> vel, <span class="keywordtype">double</span> t, <span class="keywordtype">double</span> D, <span class="keywordtype">double</span> dx)
<a name="l00237"></a>00237 {
<a name="l00238"></a>00238     <span class="keywordtype">double</span> x;
<a name="l00239"></a>00239     <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i = Ta.lbound(firstDim); i &lt;= Ta.ubound(firstDim); ++i) {
<a name="l00240"></a>00240       x = i * dx;
<a name="l00241"></a>00241       Ta(i) = 0.5 * ( erfc( 0.5 * (x - vel * t) / sqrt(D * t) ) + 
<a name="l00242"></a>00242                       exp(vel * x) * exp(-D) * 
<a name="l00243"></a>00243                       erfc( 0.5 * (x + vel * t) / sqrt(D * t)) );
<a name="l00244"></a>00244     }
<a name="l00245"></a>00245 }
<a name="l00246"></a>00246 
<a name="l00247"></a>00247 
<a name="l00248"></a>00248 
<a name="l00249"></a>00249 
<a name="l00250"></a>00250 
</pre></div></div>
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